Fundamentals of Sensors for Engineering and Science

48 Fundamentals of Sensors for Engineering and Science

moves upward and the other leg downward). Thus, the total torque equals

2F

C

h, where h is the lateral distance between the two legs of the tube. Not-

ing that the mass flow rate of the fluid, ˙m = ρUA, the mass flow rate can

be related to the frequency by

˙m =

T

2Lhω

. (2.49)

This can be expressed in terms of the twist displacement angle, θ

tw

, by

noting that θ

tw

= T/K, where K is the elastic stiffness of the tube. Thus,

Equation 2.49 becomes

˙m =

Kθ

2Lhω

. (2.50)

The twist displacement angle usually is small, such that sin θ ' θ '

∆y/(h/2), where ∆y is the vertical displacement normal to the plane of

the tube